Algebra worksheet — GCSE Foundation

1.Factorise fully 5x + 5y − 5

2.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

3.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

4.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

5.p = 4. Work out the value of 2p³.

6.Which expression means 'triple c, then add double d'?

7.The diagram shows the graph of a function. Which equation could it represent?

8.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

9.Make x the subject of the formula y = 2x − 9.

10.A number machine multiplies its input by 3. The output is 15. Work out the input.

11.Which expression is equivalent to 7x − 3(2x − 6)?

12.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

13.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

14.Which of these statements is an equation with exactly one solution?

15.Write down the expression that means the same as m² × m × 3.